Heater Core or Water Pump?

'98 Chevy Lumina. Driving at Highway speed, I hear a short rattle. Makes me think of linkages vibrating, from the passenger area. Few minutes later I hear it again. Few minutes later I look down to see me thermostat at 240+. I watch it redline, hold for a few minutes, then the rattle again and my temp goes down to 160 or so. All of this happens at 60 mph, in 45 degree weather. Rinse, repeat about every 10-15 minutes. I notice that while the engine temp is climbing, I have no hot air from the vents and after the rattle and temp drop I do have hot air. Check the block when I get home and I see the familiar green puddles. So is this: Water pump, the apparent source of the leaks, heater core causing back pressure to leak at the hose, or the ever dreaded head gasket?

I think it’s the water pump.
I’ve seen them leak only when spinning.
Start the car from cold and watch under the hood as it warms up.
The rattle is probably air bubbles in the cooling system.
Change the radiator cap and thermostat if they’re over 5 years old.

I agree, it sounds like a water pump to me! Remove belt and try and to move pulley back and forth to see what the condition of the pump. If good, inspect pump for leaks with light and mirror if you have one.

The vibration/rattle might be the radiator cooling fan when it is running. Check the blades to make sure the aren’t bent or mssing a piece of the fan.

I have seen cooling fans with mud stuck in them and when they run the whole car shakes.